\begin{tabular}{l}
\text{\LARGE{Geometric distribution}}\\
\\\hline\\
\text{Geometric distribution is a discrete probability distribution of the number of}\\
\text{Bernoulli trials needed to get the first success. In other words, it expresses the}\\
\text{probability that the first occurence of success requires exactly }k\text{ number of}\\
\text{independent trials.}\\
\text{There is also another interpretation of geometric distribution which pertains}\\
\text{to the number of failures before the first success. However, it is not considered}\\
\text{in this application.}
\\\\\hline\\
\text{\Large{Input parameters}}\\
    \begin{array}{ll}\\
    \\p & \text{probability of success in a single trial}\\
    \end{array}
\\\\\hline\\
\text{\Large{Output parameters}}\\
    \begin{array}{ll}\\
    \\\text{Expected value} & \mathbf{\frac{1}{p}}\\
    \\\text{Standard deviation} & \mathbf{\frac{\sqrt{1-p}}{p}}\\
    \\\text{Variance} & \mathbf{\frac{1-p}{p^2}}\\
    \end{array}
\\\\\hline\\
\text{\Large{Additional information}}\\
    \begin{array}{ll}\\
    \\\text{Probability mass function} & \mathbf{\left(1-p\right)^{k-1}p}\\
    \\\text{Moment-generating function} & \mathbf{\frac{pe^t}{1-\left(1-p\right)e^t}}\\
    \end{array}
\end{tabular}